Geodesic
Commutators of flows and fields
Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 229-236 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The well known formula $[X,Y]=\tfrac{1}{2}\tfrac{\partial ^2}{\partial t^2}|_0 (^Y_{-t}ø^X_{-t}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
The well known formula $[X,Y]=\tfrac{1}{2}\tfrac{\partial ^2}{\partial t^2}|_0 (^Y_{-t}ø^X_{-t}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
Classification : 37C10, 58F25
Keywords: commutators; flows; vector fields 
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     author = {Mauhart, Markus and Michor, Peter W.},
     title = {Commutators of flows and fields},
     journal = {Archivum mathematicum},
     pages = {229--236},
     year = {1992},
     volume = {28},
     number = {3-4},
     mrnumber = {1222291},
     zbl = {0784.58051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1992_28_3-4_a11/}
}
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Mauhart, Markus; Michor, Peter W. Commutators of flows and fields. Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 229-236. http://geodesic.mathdoc.fr/item/ARM_1992_28_3-4_a11/